Multiply.
$2 \frac{1}{2} \times 2 \frac{1}{3}$
Write your answer as a mixed number.
To multiply the mixed numbers \(2 \frac{1}{2}\) and \(2 \frac{1}{3}\), we first convert each into an improper fraction. A mixed number \(a \frac{b}{c}\) can be written as \(\frac{a \times c + b}{c}\).
For the first number:
\[2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}\]
For the second number:
\[2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3}\]
Now, we multiply the two resulting improper fractions:
\[\frac{5}{2} \times \frac{7}{3} = \frac{5 \times 7}{2 \times 3} = \frac{35}{6}\]
To convert the improper fraction \(\frac{35}{6}\) back into a mixed number, we divide 35 by 6.
\(35 \div 6 = 5\) with a remainder of \(5\) (since \(6 \times 5 = 30\) and \(35 - 30 = 5\)).
Thus, \(\frac{35}{6} = 5 \frac{5}{6}\).
The result of the multiplication is \(\boxed{5 \frac{5}{6}}\).
Calculating mixed numbers is common in daily activities like baking or construction. For instance, if a recipe calls for \(2 \frac{1}{2}\) cups of flour and you decide to make \(2 \frac{1}{3}\) times the recipe for a larger gathering, you would need to calculate \(2 \frac{1}{2} \times 2 \frac{1}{3} = 5 \frac{5}{6}\) cups of flour. This skill ensures you scale your measurements accurately for perfect results.